C₂₃×#1770 #15669389

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1770

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂³
commutator	C₂²	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle, prime radical	C₂³×C₂₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27)(32,33,36,38,35,37,39,34);(25,27)(28,29,30,31)(33,37)(34,38);(32,34,39,37,35,38,36,33)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7168, C₂₃×#7170, C₂₃×#8202, …
maximal normal subgroup of	C₂₃×#7168, C₂₃×#7170, C₂₃×#8202, …
maximal quotient of	C₂₃×#8260, C₂₃×#8261, C₂₃×#8265, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 502);

C23×#1770 #15669389